1. Field of the Invention
The invention disclosed herein relates to an assessment of a material by use of nuclear magnetic resonance (NMR) and, in particular, to use of a mathematical model for two-dimensional relaxation analysis.
2. Description of the Related Art
Downhole characterization techniques are of considerable value for geophysical exploration. For example, characterization of parameters associated with geologic formations provides for insight into any reservoirs of hydrocarbons, which may be present. More specifically, knowledge of porosity and percentage of movable fluids can provide insight into the quantity of hydrocarbons that may be extracted from the formation. A number of technologies are applied downhole for in-situ determination of these parameters. These technologies include nuclear magnetic resonance (NMR) imaging.
When performing NMR imaging, vast quantities of data are obtained. The data generally includes longitudinal and transverse relaxation times that are obtained using various magnetic field gradients and/or inter-echo times. In the prior art, this data is organized into groups of data that were obtained with the same magnetic field gradient and/or inter-echo time. A two-dimensional inversion operator is then applied to each group to determine a petrophysical characteristic such as porosity. Because each data group has less data than the total amount of data, inversion of these partial data sets can lead to inadequate spectral resolution and increased uncertainty in hydrocarbon characterization.
Therefore, what are needed are techniques to improve spectral resolution and decrease uncertainty in hydrocarbon characterization when performing NMR imaging.